In a digital communication system, a transmitter typically encodes traffic data based on a forward-error correction (FEC) coding scheme to obtain code bits and further maps the code bits to modulation symbols based on a modulation scheme. The transmitter then processes the modulation symbols to generate a modulated signal and transmits this signal via a communication channel. The communication channel distorts the transmitted signal with a channel response and further degrades the signal with noise and interference.
A receiver receives the transmitted signal and processes the received signal to obtain symbols, which can be distorted and noisy versions of the modulation symbols sent by the transmitter. The receiver can then compute log-likelihood ratio (LLRs) for the code bits based on the received symbols. The LLRs are indicative of the confidence in zero (‘0’) or one (‘1’) being sent for each code bit. For a given code bit, a positive LLR value can indicate more confidence in ‘0’ being sent for the code bit, a negative LLR value can indicate more confidence in ‘1’ being sent for the code bit, and an LLR value of zero can indicate equal likelihood of ‘0’ or ‘1’ being sent for the code bit. With FEC decoder, the receiver can then decode the LLRs to obtain decoded data, which is an estimate of the traffic data sent by the transmitter.
In a soft-in soft-out (SISO) decoder, “soft” refers to the fact that the incoming and/or outgoing data can take on values other than 0 or 1, in order to indicate reliability. The soft output is the LLR for value of the bit, is used as the soft input to an outer decoder. The computation for the LLRs can be complex, leading to high power consumption. However, accurate LLRs can increase the decoding performance. There is therefore a need in the art for techniques to efficiently and accurately compute LLRs for code bits.
The computational difficulty for LLRs calculation is even more apparent for optical communication systems using block-coded high-dimensional modulation formats. For example, any digital modulation scheme uses a finite number of distinct symbols to represent digital data. For example, conventional dual-polarization binary phase-shift keying (DP-BPSK) transmits two bits on the four dimensions of the optical carrier. Two dimensions are modulated independently, and only two dimensions are utilized. However, the optical coherent communication systems are naturally suited for modulation with four-dimensional (4D) signal constellations.
Four-dimensional modulation formats can achieve substantial gains compared with conventional modulation formats such as dual-polarization quaternary phase-shift keying (DP-QPSK) and 16-ary quadrature-amplitude modulation (DP-16QAM). Polarization-switched QPSK (PS-QPSK) and set-partitioned 128-ary QAM (SP-128QAM) are known to be practical 4D constellations, and they can achieve 1.76 dB and 2.43 dB gains in asymptotic power efficiency, respectively. The achievable gain can be further improved by using higher dimensional modulation formats. For example, 24D extended Golay code achieves 6.00 dB gain by producing the block of 24 bits including 12 data bits and 12 parity bits selected to increase distance between possible symbols, which makes the LLRs calculation computationally complex.
Accordingly, there is a need to reduce computational complexity for determining LLRs for modulated symbols transmitted over a channel.